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Question Consider a circle with centre O. Line segments PL and AM are two perpendicular diameters of the circle. What is the figure APML? Reason and/or experiment to figure this out.
In the figure, PL and AM are two perpendicular diameters of the circle. Let r be the radius of the circle. ∴ PL = PO + OL = r + r = 2r and AM = AO + OM = r + r = 2r ∴ PL = AM ∴ In the quadrilateral APML, diagonals PL and AM are equal and are perpendicular to each other. Also, OP = OA = OL = OM = r ∴ Diameters PL and AM bisect each other at O. ∴ Quadrilateral APML is a square.